Class Of Diffusion Processes Research Articles

Origin of anomalous diffusion in iron mononitride thin films

We have studied the origin of a counter intuitive diffusion behavior of Fe and N atoms in a iron mononitride (FeN) thin film. It was observed that in-spite of a larger atomic size, Fe tend to diffuse more rapidly than smaller N atoms. This only happens in the N-rich region of Fe-N phase diagram, in the N-poor regions, N diffusion coefficient is orders of magnitude larger than Fe. Detailed self-diffusion measurements performed in FeN thin films reveal that the diffusion mechanism of Fe and N is different - Fe atoms diffuse through a complex process, which in addition to a volume diffusion, pre-dominantly controlled by a fast grain boundary diffusion. On the other hand N atoms diffuse through a classical volume-type diffusion process. Observed results have been explained in terms of stronger Fe-N (than Fe-Fe) bonds generally predicted theoretically for mononitride compositions of transition metals.

On the relationship between a quantum Markov semigroup and its representation via linear stochastic Schrödinger equations

A quantum Markov semigroup can be represented via classical diffusion processes solving a stochastic Schrödinger equation. In this paper we first prove that a quantum Markov semigroup is irreducible if and only if classical diffusion processes are total in the Hilbert space of the system. Then we study the relationship between irreducibility of a quantum Markov semigroup and properties of these diffusions such as accessibility, the Lie algebra rank condition, and irreducibility. We prove that all these properties are, in general, stronger than irreducibility of the quantum Markov semigroup, nevertheless, they are equivalent for some important classes of semigroups.

Diffusive mixing and Tsallis entropy.

Brownian motion, the classical diffusive process, maximizes the Boltzmann-Gibbs entropy. The Tsallis q entropy, which is nonadditive, was developed as an alternative to the classical entropy for systems which are nonergodic. A generalization of Brownian motion is provided that maximizes the Tsallis entropy rather than the Boltzmann-Gibbs entropy. This process is driven by a Brownian measure with a random diffusion coefficient. The distribution of this coefficient is derived as a function of q for 1<q<3. Applications to transport in porous media are considered.

Theoretical and Experimental Investigations of Wave-Induced Vertical Mixing

Theoretical investigations supported by a series of original laboratory experiments are conducted to study a wave-induced vertical mixing process. The derived semi-analytical solution is very efficient and is applied to predict the effects of water waves on the temperature changes and the evolution of temperature profiles. The results indicate that waves increase a mixing process. The rate of change of the temperature is higher when waves contributed to mixing process and this process increases with increasing the wavelength to water depth ratio. The analysis indicates that for typical ocean waves the contribution of water waves to mixing may be several orders of magnitude higher than a corresponding contribution arising from the classical diffusion process. This implies a need to conduct more theoretical studies and experimental investigation on the effect of water waves on mixing processes. A series of original laboratory experiments were conducted in the insulated wave flume to verify the derived model. The comparisons show a reasonable agreement between predicted and measured temperature profiles. A reasonable agreement between theoretical results and experimental data is observed for the whole considered range of initial temperature distributions. The comparisons indicate that the model is applicable even to cases when gradients in temperature distributions over water depth are fairly high.

Noncommutative martingale deviation and Poincaré type inequalities with applications

We prove a deviation inequality for noncommutative martingales by extending Oliveira's argument for random matrices. By integration we obtain a Burkholder type inequality with satisfactory constant. Using continuous time, we establish noncommutative Poincar\'e type inequalities for "nice" semigroups with a positive curvature condition. These results allow us to prove a general deviation inequality and a noncommutative transportation inequality due to Bobkov and G\"otze in the commutative case. To demonstrate our setting is general enough, we give various examples, including certain group von Neumann algebras, random matrices and classical diffusion processes, among others.

Interaction-Induced Impeding of Decoherence and Anomalous Diffusion

We study how the interplay of dissipation and interactions affects the dynamics of a bosonic many-body quantum system. In the presence of both dissipation and strongly repulsive interactions, observables such as the coherence and the density fluctuations display three dynamical regimes: an initial exponential variation followed by a power-law regime, and finally a slow exponential convergence to their asymptotic values. These very long-time scales arise as dissipation forces the population of states disfavored by interactions. The long-time, strong coupling dynamics are understood by performing a mapping onto a classical diffusion process displaying non-Brownian behavior. While both dissipation and strong interactions tend to suppress coherence when acting separately, we find that strong interaction impedes the decoherence process generated by the dissipation.

Minimum density power divergence estimator for diffusion processes

In this paper, we consider the robust estimation for a certain class of diffusion processes including the Ornstein–Uhlenbeck process based on discrete observations. As a robust estimator, we consider the minimum density power divergence estimator (MDPDE) proposed by Basu et al. (Biometrika 85:549–559, 1998). It is shown that the MDPDE is consistent and asymptotically normal. A simulation study demonstrates the strong robustness of the MDPDE.

Nonnegativity of solutions to the basic adjoint relationship for some diffusion processes

For a multi-dimensional diffusion process, an important problem is whether the associated basic adjoint relationship (BAR) uniquely characterizes the stationary distribution of the diffusion process. A key step in this characterization is an open problem that any solution to BAR does not change sign. This note describes the open problem precisely in the context of two classes of diffusion processes. They are semimartingale reflecting Brownian motions and piecewise Ornstein---Uhlenbeck processes.

Equilibration and temperature distribution in a driven ion chain

We study the non-equilibrium dynamics and equilibration in a dissipative quantum many-body system—a chain of ions with two points of the chain driven by a thermal bath under different temperatures. Instead of a simple linear temperature gradient (characterized by the local motional excitation) as one expects from a typical classical heat diffusion process, the temperature distribution in the ion chain shows surprisingly rich patterns, which depend on the rate of ion coupling to the bath, the location of driven ions and the dissipation rates of the other ions in the chain. By simulating the temperature evolution, we show that these unusual temperature distribution patterns in the ion chain can be quantitatively tested in experiments within a realistic time scale.

Exponential change of measure applied to term structures of interest rates and exchange rates

In this paper, we study the term structures of interest rates and foreign exchange rates through establishing a state-price deflator. The state-price deflator considered here can be viewed as an extension to the potential representation of the state-price density in [Rogers, L.C.G., 1997. The potential approach to the term structure of interest rates and foreign exchange rates. Mathematical Finance 7(2), 157–164]. We identify a risk-neutral probability measure from the state-price deflator by a technique of exponential change of measure for Markov processes proposed by [Palmowski, Z., Rolski, T., 2002. A technique for exponential change of measure for Markov processes. Bernoulli 8(6), 767–785] and present examples of several classes of diffusion processes (jump–diffusions and diffusions with regime-switching) to illustrate the proposed theory. A comparison between the exponential change of measure and the Esscher transform for identifying risk-neutral measures is also presented. Finally, we consider the exchange rate dynamics by virtue of the ratio of the current state-price deflators between two economies and then discuss the pricing of currency options.

Using selection bias to explain the observed structure of Internet diffusions

Recently, large datasets stored on the Internet have enabled the analysis of processes, such as large-scale diffusions of information, at new levels of detail. In a recent study, Liben-Nowell and Kleinberg [(2008) Proc Natl Acad Sci USA 105:4633-4638] observed that the flow of information on the Internet exhibits surprising patterns whereby a chain letter reaches its typical recipient through long paths of hundreds of intermediaries. We show that a basic Galton-Watson epidemic model combined with the selection bias of observing only large diffusions suffices to explain these patterns. Thus, selection biases of which data we observe can radically change the estimation of classical diffusion processes.

Entropic measure and Wasserstein diffusion

We construct a new random probability measure on the circle and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the action of smooth diffeomorphism of the sphere and the interval, respectively. The associated integration by parts formula is used to construct two classes of diffusion processes on probability measures (on the sphere or the unit interval) by Dirichlet form methods. The first one is closely related to Malliavin’s Brownian motion on the homeomorphism group. The second one is a probability valued stochastic perturbation of the heat flow, whose intrinsic metric is the quadratic Wasserstein distance. It may be regarded as the canonical diffusion process on the Wasserstein space.

Equação da difusão fracionária não-linear: solução exata

We devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms. The presence of external forces and absorbent terms is also considered. The solutions found here can have a compact or long tail behavior. Particularly in the last case in the asymptotic limit, we relate these solutions to the Levy or Tsallis distributions. In addition, from the results presented here, a rich class of diffusive processes, including normal and anomalous ones, can be obtained.

The Inability of Ambipolar Diffusion to Set a Characteristic Mass Scale in Molecular Clouds

We investigate the question of whether ambipolar diffusion (ion-neutral drift) determines the smallest length and mass scales on which structure forms in a turbulent molecular cloud. We simulate magnetized turbulence in a mostly neutral, uniformly driven, turbulent medium, using a three-dimensional, two-fluid, magnetohydrodynamics (MHD) code modified from Zeus-MP. We find that substantial structure persists below the ambipolar diffusion scale because of the propagation of compressive slow MHD waves at smaller scales. Contrary to simple scaling arguments, ambipolar diffusion thus does not suppress structure below its characteristic dissipation scale, as would be expected for a classical diffusive process. We have found this to be true for the magnetic energy, velocity, and density. Correspondingly, ambipolar diffusion leaves the clump mass spectrum unchanged. Ambipolar diffusion appears unable to set a characteristic scale for gravitational collapse and star formation in turbulent molecular clouds.

A class of processes on the path space over a compact Riemannian manifold with unbounded diffusion

A class of diffusion processes on the path space over a compact Riemannian manifold is constructed. The diffusion of such a process is governed by an unbounded operator. A representation of the associated generator is derived and the existence of a certain local second moment is shown.

The measurement problem on classical diffusion process: inverse method on stochastic processes

In a high number of diffusive systems, measures are processed to calculate material parameters such as diffusion coefficients, or to verify the accuracy of mathematical models. However, the precision of the parameter determination or of the model relevance depends on the location of the measure itself. The aim of this paper is first to analyse, for a mono-dimensional system, the precision of the measure in relation with its location by an inverse problem algorithm and secondly to examine the physical meaning of the results. Statistical mechanic considerations show that, passing over a time–distance criterion, measurement becomes uncertain whatever the initial conditions. The criterion proves that this chaotic mode is related to the production of anti-entropy at a mesoscopique scale that is in violation to quantum theory about measurement.

Dissipation and decoherence in the generalized Jaynes-Cummings model

In this paper, we present a simple approach for understanding some general aspects of the irreversible dynamics of the generalized Jaynes-Cummings model. By working in the dressed-state representation, it is possible to split the dynamics of populations and coherences. Then it can be shown that the coherence dynamics may present localization and dispersivelike decay behavior, whereas the population dynamics are characterized in terms of a classical diffusive process. These phenomena are studied by developing a perturbation theory that provides simple analytical results that could be applicable to any general source of irreversibility in the Jaynes-Cummings model. As an application, we extend and analytically characterize our previous reported results on heating and decoherence in trapped ions [Phys. Rev. A 65, 041402 (2002)].

Investigation of Radial Particle Transport in the GAMMA 10 Tandem Mirror

Radial particle transport in GAMMA 10 was investigated under a quasi-steady state condition plasma. The transport analysis was carried out with changing the boundary conditions, in order to reconstruct the density profile which is consistent with the measured data. From the above result, the best fit profile to the measured one was obtained with the diffusivity of 0.57 m2/s. The particle diffusivity in an additional gas puffing experiment was estimated. The result of the transport analysis was also compared with the diffusion coefficient expected from classical diffusion processes.

Comparing algebraic and numerical solutions of classical diffusion process equations in computational financial mathematics

We revise the interrelations between the classical Black Scholes equation, the diffusion equation and Burgers equation. Some of the algebraic properties the diffusion equation shows are elaborated and qualitatively presented. The related numerical elementary recipes are briefly elucidated in context of the diffusion equation. The quality of the approximations to the exact solutions is compared throughout the visualizations. The article mainly is based on the pedagogical style of the presentations to the Novacella Easter School 2000 on Financial Mathematics.

The time course of perceptual choice: The leaky, competing accumulator model.

The time course of perceptual choice is discussed in a model of gradual, leaky, stochastic, and competitive information accumulation in nonlinear decision units. Special cases of the model match a classical diffusion process, but leakage and competition work together to address several challenges to existing diffusion, random walk, and accumulator models. The model accounts for data from choice tasks using both time-controlled (e.g., response signal) and standard reaction time paradigms and its adequacy compares favorably with other approaches. A new paradigm that controls the time of arrival of information supporting different choice alternatives provides further support. The model captures choice behavior regardless of the number of alternatives, accounting for the log-linear relation between reaction time and number of alternatives (Hick's law) and explains a complex pattern of visual and contextual priming in visual word identification.